let 1<=r<=n. A subset of{1,2....n} of cardinality "r" is chosen at random. How do i calculate the probability that 1 is an element of the chosen subset

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- Oct 19th 2008, 06:12 AMmath8553probability
let 1<=r<=n. A subset of{1,2....n} of cardinality "r" is chosen at random. How do i calculate the probability that 1 is an element of the chosen subset

- Oct 19th 2008, 08:58 AMPlato
- Oct 19th 2008, 09:16 AMvincisonfireReply
The number of subset of cardinality r is

$\displaystyle {{n} \choose {r}}$

and the number of those that doesn't contain 1 is $\displaystyle {{n-1} \choose {r-1}}$ as Plato told you.

The probability of taking a set that doesn't contain 1 is $\displaystyle {{n-1} \choose {r-1}}/{{n} \choose {r}}$